Why is (log3 400)/2 equivalent to log3 20? Can you show me how you can prove that step by step, without a calculator? Thank you so much!

Answer 1

is
log 400 = 2 log 20 ??
well
log a^x = a log x
so
2 log 20 = log 20^2
and lo and behold
20^2 = 400

Answer 2

Oh, thank you so much! I did not think of making 400 20^2.